CONSTRUCTION OF THE ASYMPTOTICS OF THE SOLUTION OF A SINGULARLY PERTURBED NONLINEAR EQUATION WITH A SINGULAR POINT

Abstract

In this paper, the subject of research is the construction of the asymptotics of the solution of a singularly perturbed nonlinear differential equation of the second order, more specifically, the new model Lighthill’s equation of the second order. Earlier, the second-order model Lighthill’s equation was considered by the uniformization method. The solution of the problem is presented by the method of the classical small parameter, which has a limited solution in a certain interval. To determine a full-fledged solution over the entire given interval, the majorant method was used. A method of parametrization is introduced, a system of differential equations with the appropriate formulation for obtaining the asymptotics of the solution is compiled. A comparative analysis of the above two methods is made, the advantages and disadvantages of finding the asymptotics of the solution of the new model Lighthill’s equation of the second order are noted. Based on the result obtained, it can be concluded that the majorant method, the parametrization method is optimal for finding the asymptotics of the solution over the entire given interval.